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Copy pathuadc_ip.py
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2288 lines (1855 loc) · 106 KB
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# Copyright 2014-2022 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Abdelrahman Ahmed <>
# Samragni Banerjee <samragnibanerjee4@gmail.com>
# James Serna <jamcar456@gmail.com>
# Terrence Stahl <>
# Ning-Yuan Chen <cny003@outlook.com>
# Alexander Sokolov <alexander.y.sokolov@gmail.com>
#
'''
Unrestricted algebraic diagrammatic construction
'''
import numpy as np
from pyscf import lib, symm
from pyscf.lib import logger
from pyscf.adc import uadc
from pyscf.adc import uadc_ao2mo
from pyscf.adc import radc_ao2mo
from pyscf.adc import dfadc
from pyscf.data.nist import HARTREE2EV
def get_imds(adc, eris=None):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(adc.stdout, adc.verbose)
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
method = adc.method
t1 = adc.t1
t2 = adc.t2
nocc_a = adc.nocc_a
nocc_b = adc.nocc_b
e_occ_a = adc.mo_energy_a[:nocc_a]
e_occ_b = adc.mo_energy_b[:nocc_b]
idn_occ_a = np.identity(nocc_a)
idn_occ_b = np.identity(nocc_b)
if eris is None:
eris = adc.transform_integrals()
eris_ovvo = eris.ovvo
eris_OVVO = eris.OVVO
eris_ovVO = eris.ovVO
eris_OVvo = eris.OVvo
# i-j block
# Zeroth-order terms
M_ij_a = lib.einsum('ij,j->ij', idn_occ_a ,e_occ_a)
M_ij_b = lib.einsum('ij,j->ij', idn_occ_b ,e_occ_b)
# Second-order terms
t2_1_a = t2[0][0][:]
M_ij_a += 0.5 * 0.5 * lib.einsum('ilde,jdel->ij',t2_1_a, eris_ovvo, optimize=True)
M_ij_a -= 0.5 * 0.5 * lib.einsum('ilde,jedl->ij',t2_1_a, eris_ovvo, optimize=True)
M_ij_a += 0.5 * 0.5 * lib.einsum('jlde,idel->ij',t2_1_a, eris_ovvo, optimize=True)
M_ij_a -= 0.5 * 0.5 * lib.einsum('jlde,ldei->ij',t2_1_a, eris_ovvo, optimize=True)
t2_1_b = t2[0][2][:]
M_ij_b += 0.5 * 0.5 * lib.einsum('ilde,jdel->ij',t2_1_b, eris_OVVO, optimize=True)
M_ij_b -= 0.5 * 0.5 * lib.einsum('ilde,jedl->ij',t2_1_b, eris_OVVO, optimize=True)
M_ij_b += 0.5 * 0.5 * lib.einsum('jlde,idel->ij',t2_1_b, eris_OVVO, optimize=True)
M_ij_b -= 0.5 * 0.5 * lib.einsum('jlde,ldei->ij',t2_1_b, eris_OVVO, optimize=True)
t2_1_ab = t2[0][1][:]
M_ij_a += 0.5 * lib.einsum('ilde,jdel->ij',t2_1_ab, eris_ovVO, optimize=True)
M_ij_b += 0.5 * lib.einsum('lied,ledj->ij',t2_1_ab, eris_ovVO, optimize=True)
M_ij_a += 0.5 * lib.einsum('jlde,idel->ij',t2_1_ab, eris_ovVO, optimize=True)
M_ij_b += 0.5 * lib.einsum('ljed,ledi->ij',t2_1_ab, eris_ovVO, optimize=True)
del t2_1_ab
# Third-order terms
if (method == "adc(3)"):
t1_2_a, t1_2_b = t1[0]
eris_oovv = eris.oovv
eris_OOVV = eris.OOVV
eris_ooVV = eris.ooVV
eris_OOvv = eris.OOvv
eris_ovvo = eris.ovvo
eris_OVVO = eris.OVVO
eris_ovVO = eris.ovVO
eris_OVvo = eris.OVvo
eris_ovoo = eris.ovoo
eris_OVOO = eris.OVOO
eris_ovOO = eris.ovOO
eris_OVoo = eris.OVoo
eris_oooo = eris.oooo
eris_OOOO = eris.OOOO
eris_ooOO = eris.ooOO
M_ij_a += lib.einsum('ld,ldji->ij',t1_2_a, eris_ovoo, optimize=True)
M_ij_a -= lib.einsum('ld,jdli->ij',t1_2_a, eris_ovoo, optimize=True)
M_ij_a += lib.einsum('ld,ldji->ij',t1_2_b, eris_OVoo, optimize=True)
M_ij_b += lib.einsum('ld,ldji->ij',t1_2_b, eris_OVOO, optimize=True)
M_ij_b -= lib.einsum('ld,jdli->ij',t1_2_b, eris_OVOO, optimize=True)
M_ij_b += lib.einsum('ld,ldji->ij',t1_2_a, eris_ovOO, optimize=True)
M_ij_a += lib.einsum('ld,ldij->ij',t1_2_a, eris_ovoo, optimize=True)
M_ij_a -= lib.einsum('ld,idlj->ij',t1_2_a, eris_ovoo, optimize=True)
M_ij_a += lib.einsum('ld,ldij->ij',t1_2_b, eris_OVoo, optimize=True)
M_ij_b += lib.einsum('ld,ldij->ij',t1_2_b, eris_OVOO, optimize=True)
M_ij_b -= lib.einsum('ld,idlj->ij',t1_2_b, eris_OVOO, optimize=True)
M_ij_b += lib.einsum('ld,ldij->ij',t1_2_a, eris_ovOO, optimize=True)
t2_1_a = t2[0][0][:]
t2_2_a = t2[1][0][:]
M_ij_a += 0.5 * 0.5* lib.einsum('ilde,jdel->ij',t2_2_a, eris_ovvo, optimize=True)
M_ij_a -= 0.5 * 0.5* lib.einsum('ilde,jedl->ij',t2_2_a, eris_ovvo, optimize=True)
M_ij_a += 0.5 * 0.5* lib.einsum('jlde,ledi->ij',t2_2_a, eris_ovvo, optimize=True)
M_ij_a -= 0.5 * 0.5* lib.einsum('jlde,iedl->ij',t2_2_a, eris_ovvo, optimize=True)
t2_1_b = t2[0][2][:]
t2_2_b = t2[1][2][:]
M_ij_b += 0.5 * 0.5* lib.einsum('ilde,jdel->ij',t2_2_b, eris_OVVO, optimize=True)
M_ij_b -= 0.5 * 0.5* lib.einsum('ilde,jedl->ij',t2_2_b, eris_OVVO, optimize=True)
M_ij_b += 0.5 * 0.5* lib.einsum('jlde,ledi->ij',t2_2_b, eris_OVVO, optimize=True)
M_ij_b -= 0.5 * 0.5* lib.einsum('jlde,iedl->ij',t2_2_b, eris_OVVO, optimize=True)
t2_1_ab = t2[0][1][:]
t2_2_ab = t2[1][1][:]
M_ij_a += 0.5 * lib.einsum('ilde,jdel->ij',t2_2_ab, eris_ovVO, optimize=True)
M_ij_b += 0.5 * lib.einsum('lied,ledj->ij',t2_2_ab, eris_ovVO, optimize=True)
M_ij_a += 0.5 * lib.einsum('jlde,ledi->ij',t2_2_ab, eris_OVvo, optimize=True)
M_ij_b += 0.5 * lib.einsum('ljed,ledi->ij',t2_2_ab, eris_ovVO, optimize=True)
t2_1_a = t2[0][0][:]
M_ij_t = lib.einsum('lmde,jldf->mejf', t2_1_a, t2_1_a, optimize=True)
M_ij_a -= 0.5 * lib.einsum('mejf,mefi->ij',M_ij_t, eris_ovvo, optimize=True)
M_ij_a -= 0.5 * lib.einsum('mejf,mefi->ji',M_ij_t, eris_ovvo, optimize=True)
M_ij_a += 0.5 * lib.einsum('mejf,mife->ij',M_ij_t, eris_oovv, optimize=True)
M_ij_a += 0.5 * lib.einsum('mejf,mife->ji',M_ij_t, eris_oovv, optimize=True)
del M_ij_t
M_ij_a += 0.5 * 0.25*lib.einsum('lmde,jnde,limn->ij',t2_1_a,
t2_1_a,eris_oooo, optimize=True)
M_ij_a -= 0.5 * 0.25*lib.einsum('lmde,jnde,lnmi->ij',t2_1_a,
t2_1_a,eris_oooo, optimize=True)
M_ij_a += 0.5 *0.25*lib.einsum('inde,lmde,jlnm->ij',t2_1_a, t2_1_a,eris_oooo, optimize=True)
M_ij_a -= 0.5 *0.25*lib.einsum('inde,lmde,jmnl->ij',t2_1_a, t2_1_a,eris_oooo, optimize=True)
M_ij_a += 0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ij_a -= 0.5*lib.einsum('lmdf,lmde,jfei->ij',t2_1_a, t2_1_a, eris_ovvo, optimize=True)
M_ij_b +=0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_a, t2_1_a, eris_OOvv , optimize=True)
M_ij_a -= 0.5*lib.einsum('lnde,lmde,jinm->ij',t2_1_a, t2_1_a, eris_oooo, optimize=True)
M_ij_a += 0.5*lib.einsum('lnde,lmde,jmni->ij',t2_1_a, t2_1_a, eris_oooo, optimize=True)
M_ij_b -= 0.5 * lib.einsum('lnde,lmde,nmji->ij',t2_1_a, t2_1_a, eris_ooOO, optimize=True)
t2_1_ab = t2[0][1][:]
M_ij_a -= 0.5 * lib.einsum('lmde,jldf,mefi->ij',t2_1_ab, t2_1_a, eris_OVvo,optimize=True)
M_ij_b += 0.5 * lib.einsum('lmde,ljdf,mefi->ij',t2_1_a, t2_1_ab, eris_ovVO ,optimize=True)
M_ij_a -= 0.5 * lib.einsum('lmde,ildf,mefj->ij',t2_1_ab, t2_1_a, eris_OVvo,optimize=True)
M_ij_b += 0.5 * lib.einsum('lmde,lidf,mefj->ij',t2_1_a, t2_1_ab, eris_ovVO ,optimize=True)
del t2_1_a
t2_1_b = t2[0][2][:]
M_ij_a += 0.5 * lib.einsum('lmde,jlfd,mefi->ij',t2_1_b, t2_1_ab, eris_OVvo ,optimize=True)
M_ij_b -= 0.5 * lib.einsum('mled,jldf,mefi->ij',t2_1_ab, t2_1_b, eris_ovVO,optimize=True)
M_ij_a += 0.5 * lib.einsum('lmde,ilfd,mefj->ij',t2_1_b, t2_1_ab, eris_OVvo ,optimize=True)
M_ij_b -= 0.5 * lib.einsum('mled,ildf,mefj->ij',t2_1_ab, t2_1_b, eris_ovVO,optimize=True)
M_ij_t = lib.einsum('lmde,jldf->mejf', t2_1_b, t2_1_b, optimize=True)
M_ij_b -= 0.5 * lib.einsum('mejf,mefi->ij',M_ij_t, eris_OVVO, optimize=True)
M_ij_b -= 0.5 * lib.einsum('mejf,mefi->ji',M_ij_t, eris_OVVO, optimize=True)
M_ij_b += 0.5 * lib.einsum('mejf,mife->ij',M_ij_t, eris_OOVV, optimize=True)
M_ij_b += 0.5 * lib.einsum('mejf,mife->ji',M_ij_t, eris_OOVV, optimize=True)
del M_ij_t
M_ij_b += 0.5 * 0.25*lib.einsum('lmde,jnde,limn->ij',t2_1_b,
t2_1_b,eris_OOOO, optimize=True)
M_ij_b -= 0.5 * 0.25*lib.einsum('lmde,jnde,lnmi->ij',t2_1_b,
t2_1_b,eris_OOOO, optimize=True)
M_ij_b += 0.5 * 0.25*lib.einsum('inde,lmde,jlnm->ij',t2_1_b,
t2_1_b,eris_OOOO, optimize=True)
M_ij_b -= 0.5 * 0.25*lib.einsum('inde,lmde,jmnl->ij',t2_1_b,
t2_1_b,eris_OOOO, optimize=True)
M_ij_a += 0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_b, t2_1_b, eris_ooVV , optimize=True)
M_ij_b += 0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_b, t2_1_b, eris_OOVV , optimize=True)
M_ij_b -= 0.5*lib.einsum('lmdf,lmde,jfei->ij',t2_1_b, t2_1_b, eris_OVVO , optimize=True)
M_ij_a -= 0.5 * lib.einsum('lnde,lmde,jinm->ij',t2_1_b, t2_1_b, eris_ooOO, optimize=True)
M_ij_b -= 0.5*lib.einsum('lnde,lmde,jinm->ij',t2_1_b, t2_1_b, eris_OOOO, optimize=True)
M_ij_b += 0.5*lib.einsum('lnde,lmde,jmni->ij',t2_1_b, t2_1_b, eris_OOOO, optimize=True)
del t2_1_b
t2_1_ab = t2[0][1][:]
M_ij_a += 0.5 * lib.einsum('mled,jlfd,mefi->ij',t2_1_ab, t2_1_ab, eris_ovvo ,optimize=True)
M_ij_a -= 0.5 * lib.einsum('mled,jlfd,mife->ij',t2_1_ab, t2_1_ab, eris_oovv ,optimize=True)
M_ij_a -= 0.5 * lib.einsum('mlde,jldf,mife->ij',t2_1_ab, t2_1_ab, eris_ooVV ,optimize=True)
M_ij_b += 0.5 * lib.einsum('lmde,ljdf,mefi->ij',t2_1_ab, t2_1_ab, eris_OVVO,optimize=True)
M_ij_b -= 0.5 * lib.einsum('lmde,ljdf,mife->ij',t2_1_ab, t2_1_ab, eris_OOVV,optimize=True)
M_ij_b -= 0.5 * lib.einsum('lmed,ljfd,mife->ij',t2_1_ab, t2_1_ab, eris_OOvv ,optimize=True)
M_ij_a += 0.5 * lib.einsum('mled,ilfd,mefj->ij',t2_1_ab, t2_1_ab, eris_ovvo ,optimize=True)
M_ij_a -= 0.5 * lib.einsum('mled,ilfd,mjfe->ij',t2_1_ab, t2_1_ab, eris_oovv ,optimize=True)
M_ij_a -= 0.5 * lib.einsum('mlde,ildf,mjfe->ij',t2_1_ab, t2_1_ab, eris_ooVV ,optimize=True)
M_ij_b += 0.5 * lib.einsum('lmde,lidf,mefj->ij',t2_1_ab, t2_1_ab, eris_OVVO ,optimize=True)
M_ij_b -= 0.5 * lib.einsum('lmde,lidf,mjfe->ij',t2_1_ab, t2_1_ab, eris_OOVV ,optimize=True)
M_ij_b -= 0.5 * lib.einsum('lmed,lifd,mjfe->ij',t2_1_ab, t2_1_ab, eris_OOvv ,optimize=True)
M_ij_a += 0.5 * lib.einsum('lmde,jnde,limn->ij',t2_1_ab ,t2_1_ab,eris_ooOO, optimize=True)
M_ij_b += 0.5 * lib.einsum('mled,njed,mnli->ij',t2_1_ab ,t2_1_ab,eris_ooOO, optimize=True)
M_ij_a +=0.5 * lib.einsum('inde,lmde,jlnm->ij',t2_1_ab, t2_1_ab,eris_ooOO, optimize=True)
M_ij_b +=0.5 * lib.einsum('nied,mled,nmjl->ij',t2_1_ab, t2_1_ab,eris_ooOO, optimize=True)
M_ij_a +=lib.einsum('mlfd,mled,jief->ij',t2_1_ab, t2_1_ab, eris_oovv , optimize=True)
M_ij_a -=lib.einsum('mlfd,mled,jfei->ij',t2_1_ab, t2_1_ab, eris_ovvo , optimize=True)
M_ij_a +=lib.einsum('lmdf,lmde,jief->ij',t2_1_ab, t2_1_ab, eris_ooVV , optimize=True)
M_ij_b +=lib.einsum('lmdf,lmde,jief->ij',t2_1_ab, t2_1_ab, eris_OOVV , optimize=True)
M_ij_b -=lib.einsum('lmdf,lmde,jfei->ij',t2_1_ab, t2_1_ab, eris_OVVO , optimize=True)
M_ij_b +=lib.einsum('lmfd,lmed,jief->ij',t2_1_ab, t2_1_ab, eris_OOvv , optimize=True)
M_ij_a -= lib.einsum('nled,mled,jinm->ij',t2_1_ab, t2_1_ab, eris_oooo, optimize=True)
M_ij_a += lib.einsum('nled,mled,jmni->ij',t2_1_ab, t2_1_ab, eris_oooo, optimize=True)
M_ij_a -= lib.einsum('lnde,lmde,jinm->ij',t2_1_ab, t2_1_ab, eris_ooOO, optimize=True)
M_ij_b -= lib.einsum('lnde,lmde,jinm->ij',t2_1_ab, t2_1_ab, eris_OOOO, optimize=True)
M_ij_b += lib.einsum('lnde,lmde,jmni->ij',t2_1_ab, t2_1_ab, eris_OOOO, optimize=True)
M_ij_b -= lib.einsum('nled,mled,nmji->ij',t2_1_ab, t2_1_ab, eris_ooOO, optimize=True)
del t2_1_ab
M_ij = (M_ij_a, M_ij_b)
cput0 = log.timer_debug1("Completed M_ab ADC(3) calculation", *cput0)
return M_ij
def get_diag(adc,M_ij=None,eris=None):
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
if M_ij is None:
M_ij = adc.get_imds()
M_ij_a, M_ij_b = M_ij[0], M_ij[1]
nocc_a = adc.nocc_a
nocc_b = adc.nocc_b
nvir_a = adc.nvir_a
nvir_b = adc.nvir_b
n_singles_a = nocc_a
n_singles_b = nocc_b
n_doubles_aaa = nocc_a * (nocc_a - 1) * nvir_a // 2
n_doubles_bab = nvir_b * nocc_a * nocc_b
n_doubles_aba = nvir_a * nocc_b * nocc_a
n_doubles_bbb = nocc_b * (nocc_b - 1) * nvir_b // 2
dim = n_singles_a + n_singles_b + n_doubles_aaa + n_doubles_bab + n_doubles_aba + n_doubles_bbb
e_occ_a = adc.mo_energy_a[:nocc_a]
e_occ_b = adc.mo_energy_b[:nocc_b]
e_vir_a = adc.mo_energy_a[nocc_a:]
e_vir_b = adc.mo_energy_b[nocc_b:]
ij_ind_a = np.tril_indices(nocc_a, k=-1)
ij_ind_b = np.tril_indices(nocc_b, k=-1)
s_a = 0
f_a = n_singles_a
s_b = f_a
f_b = s_b + n_singles_b
s_aaa = f_b
f_aaa = s_aaa + n_doubles_aaa
s_bab = f_aaa
f_bab = s_bab + n_doubles_bab
s_aba = f_bab
f_aba = s_aba + n_doubles_aba
s_bbb = f_aba
f_bbb = s_bbb + n_doubles_bbb
d_ij_a = e_occ_a[:,None] + e_occ_a
d_a_a = e_vir_a[:,None]
D_n_a = -d_a_a + d_ij_a.reshape(-1)
D_n_a = D_n_a.reshape((nvir_a,nocc_a,nocc_a))
D_aij_a = D_n_a.copy()[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
d_ij_b = e_occ_b[:,None] + e_occ_b
d_a_b = e_vir_b[:,None]
D_n_b = -d_a_b + d_ij_b.reshape(-1)
D_n_b = D_n_b.reshape((nvir_b,nocc_b,nocc_b))
D_aij_b = D_n_b.copy()[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
d_ij_ab = e_occ_b[:,None] + e_occ_a
d_a_b = e_vir_b[:,None]
D_n_bab = -d_a_b + d_ij_ab.reshape(-1)
D_aij_bab = D_n_bab.reshape(-1)
d_ij_ab = e_occ_a[:,None] + e_occ_b
d_a_a = e_vir_a[:,None]
D_n_aba = -d_a_a + d_ij_ab.reshape(-1)
D_aij_aba = D_n_aba.reshape(-1)
diag = np.zeros(dim)
# Compute precond in h1-h1 block
M_ij_a_diag = np.diagonal(M_ij_a)
M_ij_b_diag = np.diagonal(M_ij_b)
diag[s_a:f_a] = M_ij_a_diag.copy()
diag[s_b:f_b] = M_ij_b_diag.copy()
# Compute precond in 2p1h-2p1h block
diag[s_aaa:f_aaa] = D_aij_a.copy()
diag[s_bab:f_bab] = D_aij_bab.copy()
diag[s_aba:f_aba] = D_aij_aba.copy()
diag[s_bbb:f_bbb] = D_aij_b.copy()
# ###### Additional terms for the preconditioner ####
# if (method == "adc(2)-x" or method == "adc(3)"):
#
# if eris is None:
# eris = adc.transform_integrals()
#
# if isinstance(eris.vvvv_p, np.ndarray):
#
# eris_oooo = eris.oooo
# eris_OOOO = eris.OOOO
# eris_ooOO = eris.ooOO
# eris_oovv = eris.oovv
# eris_OOVV = eris.OOVV
# eris_ooVV = eris.ooVV
# eris_OOvv = eris.OOvv
# eris_ovvo = eris.ovvo
# eris_OVVO = eris.OVVO
#
# eris_oooo_p = np.ascontiguousarray(eris_oooo.transpose(0,2,1,3))
# eris_oooo_p -= np.ascontiguousarray(eris_oooo_p.transpose(0,1,3,2))
# eris_oooo_p = eris_oooo_p.reshape(nocc_a*nocc_a, nocc_a*nocc_a)
#
# temp = np.zeros((nvir_a,eris_oooo_p.shape[0]))
# temp[:] += np.diagonal(eris_oooo_p)
# temp = temp.reshape(nvir_a, nocc_a, nocc_a)
# diag[s_aaa:f_aaa] += -temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
#
# eris_OOOO_p = np.ascontiguousarray(eris_OOOO.transpose(0,2,1,3))
# eris_OOOO_p -= np.ascontiguousarray(eris_OOOO_p.transpose(0,1,3,2))
# eris_OOOO_p = eris_OOOO_p.reshape(nocc_b*nocc_b, nocc_b*nocc_b)
#
# temp = np.zeros((nvir_b,eris_OOOO_p.shape[0]))
# temp[:] += np.diagonal(eris_OOOO_p)
# temp = temp.reshape(nvir_b, nocc_b, nocc_b)
# diag[s_bbb:f_bbb] += -temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
#
# eris_oOoO_p = np.ascontiguousarray(eris_ooOO.transpose(0,2,1,3))
# eris_oOoO_p = eris_oOoO_p.reshape(nocc_a*nocc_b, nocc_a*nocc_b)
#
# temp = np.zeros((nvir_b, eris_oOoO_p.shape[0]))
# temp[:] += np.diag(eris_oOoO_p)
# diag[s_bab:f_bab] += -temp.reshape(-1)
#
# temp = np.zeros((nvir_a, eris_oOoO_p.shape[0]))
# temp[:] += np.diag(eris_oOoO_p.T)
# diag[s_aba:f_aba] += -temp.reshape(-1)
#
# eris_ovov_p = np.ascontiguousarray(eris_oovv.transpose(0,2,1,3))
# eris_ovov_p -= np.ascontiguousarray(eris_ovvo.transpose(0,2,3,1))
# eris_ovov_p = eris_ovov_p.reshape(nocc_a*nvir_a, nocc_a*nvir_a)
#
# temp = np.zeros((nocc_a,nocc_a,nvir_a))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc_a,nvir_a)
# temp = np.ascontiguousarray(temp.T)
# diag[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
#
# temp = np.ascontiguousarray(temp.transpose(0,2,1))
# diag[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
#
# eris_OVOV_p = np.ascontiguousarray(eris_OOVV.transpose(0,2,1,3))
# eris_OVOV_p -= np.ascontiguousarray(eris_OVVO.transpose(0,2,3,1))
# eris_OVOV_p = eris_OVOV_p.reshape(nocc_b*nvir_b, nocc_b*nvir_b)
#
# temp = np.zeros((nocc_b,nocc_b,nvir_b))
# temp[:] += np.diagonal(eris_OVOV_p).reshape(nocc_b,nvir_b)
# temp = np.ascontiguousarray(temp.T)
# diag[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
#
# temp = np.ascontiguousarray(temp.transpose(0,2,1))
# diag[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
#
# temp = np.zeros((nocc_a, nocc_b, nvir_b))
# temp[:] += np.diagonal(eris_OVOV_p).reshape(nocc_b, nvir_b)
# temp = np.ascontiguousarray(temp.transpose(2,0,1))
# diag[s_bab:f_bab] += temp.reshape(-1)
#
# temp = np.zeros((nocc_b, nocc_a, nvir_a))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc_a, nvir_a)
# temp = np.ascontiguousarray(temp.transpose(2,0,1))
# diag[s_aba:f_aba] += temp.reshape(-1)
#
# eris_oVoV_p = np.ascontiguousarray(eris_ooVV.transpose(0,2,1,3))
# eris_oVoV_p = eris_oVoV_p.reshape(nocc_a*nvir_b, nocc_a*nvir_b)
#
# temp = np.zeros((nocc_b, nocc_a, nvir_b))
# temp[:] += np.diagonal(eris_oVoV_p).reshape(nocc_a,nvir_b)
# temp = np.ascontiguousarray(temp.transpose(2,1,0))
# diag[s_bab:f_bab] += temp.reshape(-1)
#
# eris_OvOv_p = np.ascontiguousarray(eris_OOvv.transpose(0,2,1,3))
# eris_OvOv_p = eris_OvOv_p.reshape(nocc_b*nvir_a, nocc_b*nvir_a)
#
# temp = np.zeros((nocc_a, nocc_b, nvir_a))
# temp[:] += np.diagonal(eris_OvOv_p).reshape(nocc_b,nvir_a)
# temp = np.ascontiguousarray(temp.transpose(2,1,0))
# diag[s_aba:f_aba] += temp.reshape(-1)
# else:
# raise Exception("Precond not available for out-of-core and density-fitted algo")
diag = -diag
return diag
def matvec(adc, M_ij=None, eris=None):
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
method = adc.method
nocc_a = adc.nocc_a
nocc_b = adc.nocc_b
nvir_a = adc.nvir_a
nvir_b = adc.nvir_b
ij_ind_a = np.tril_indices(nocc_a, k=-1)
ij_ind_b = np.tril_indices(nocc_b, k=-1)
n_singles_a = nocc_a
n_singles_b = nocc_b
n_doubles_aaa = nocc_a * (nocc_a - 1) * nvir_a // 2
n_doubles_bab = nvir_b * nocc_a * nocc_b
n_doubles_aba = nvir_a * nocc_b * nocc_a
n_doubles_bbb = nocc_b * (nocc_b - 1) * nvir_b // 2
dim = n_singles_a + n_singles_b + n_doubles_aaa + n_doubles_bab + n_doubles_aba + n_doubles_bbb
e_occ_a = adc.mo_energy_a[:nocc_a]
e_occ_b = adc.mo_energy_b[:nocc_b]
e_vir_a = adc.mo_energy_a[nocc_a:]
e_vir_b = adc.mo_energy_b[nocc_b:]
if eris is None:
eris = adc.transform_integrals()
d_ij_a = e_occ_a[:,None] + e_occ_a
d_a_a = e_vir_a[:,None]
D_n_a = -d_a_a + d_ij_a.reshape(-1)
D_n_a = D_n_a.reshape((nvir_a,nocc_a,nocc_a))
D_aij_a = D_n_a.copy()[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
d_ij_b = e_occ_b[:,None] + e_occ_b
d_a_b = e_vir_b[:,None]
D_n_b = -d_a_b + d_ij_b.reshape(-1)
D_n_b = D_n_b.reshape((nvir_b,nocc_b,nocc_b))
D_aij_b = D_n_b.copy()[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
d_ij_ab = e_occ_b[:,None] + e_occ_a
d_a_b = e_vir_b[:,None]
D_n_bab = -d_a_b + d_ij_ab.reshape(-1)
D_aij_bab = D_n_bab.reshape(-1)
d_ij_ab = e_occ_a[:,None] + e_occ_b
d_a_a = e_vir_a[:,None]
D_n_aba = -d_a_a + d_ij_ab.reshape(-1)
D_aij_aba = D_n_aba.reshape(-1)
s_a = 0
f_a = n_singles_a
s_b = f_a
f_b = s_b + n_singles_b
s_aaa = f_b
f_aaa = s_aaa + n_doubles_aaa
s_bab = f_aaa
f_bab = s_bab + n_doubles_bab
s_aba = f_bab
f_aba = s_aba + n_doubles_aba
s_bbb = f_aba
f_bbb = s_bbb + n_doubles_bbb
if M_ij is None:
M_ij = adc.get_imds()
M_ij_a, M_ij_b = M_ij
#Calculate sigma vector
def sigma_(r):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(adc.stdout, adc.verbose)
s = np.zeros(dim)
r_a = r[s_a:f_a]
r_b = r[s_b:f_b]
r_aaa = r[s_aaa:f_aaa]
r_bab = r[s_bab:f_bab]
r_aba = r[s_aba:f_aba]
r_bbb = r[s_bbb:f_bbb]
r_aaa = r_aaa.reshape(nvir_a,-1)
r_bbb = r_bbb.reshape(nvir_b,-1)
r_aaa_u = None
r_aaa_u = np.zeros((nvir_a,nocc_a,nocc_a))
r_aaa_u[:,ij_ind_a[0],ij_ind_a[1]]= r_aaa.copy()
r_aaa_u[:,ij_ind_a[1],ij_ind_a[0]]= -r_aaa.copy()
r_bbb_u = None
r_bbb_u = np.zeros((nvir_b,nocc_b,nocc_b))
r_bbb_u[:,ij_ind_b[0],ij_ind_b[1]]= r_bbb.copy()
r_bbb_u[:,ij_ind_b[1],ij_ind_b[0]]= -r_bbb.copy()
r_aba = r_aba.reshape(nvir_a,nocc_a,nocc_b)
r_bab = r_bab.reshape(nvir_b,nocc_b,nocc_a)
eris_ovoo = eris.ovoo
eris_OVOO = eris.OVOO
eris_OVoo = eris.OVoo
eris_ovOO = eris.ovOO
############ ADC(2) ij block ############################
s[s_a:f_a] = lib.einsum('ij,j->i',M_ij_a,r_a)
s[s_b:f_b] = lib.einsum('ij,j->i',M_ij_b,r_b)
############# ADC(2) i - kja block #########################
s[s_a:f_a] += 0.5*lib.einsum('jaki,ajk->i', eris_ovoo, r_aaa_u, optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('kaji,ajk->i', eris_ovoo, r_aaa_u, optimize=True)
s[s_a:f_a] += lib.einsum('jaki,ajk->i', eris_OVoo, r_bab, optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('jaki,ajk->i', eris_OVOO, r_bbb_u, optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('kaji,ajk->i', eris_OVOO, r_bbb_u, optimize=True)
s[s_b:f_b] += lib.einsum('jaki,ajk->i', eris_ovOO, r_aba, optimize=True)
############## ADC(2) ajk - i block ############################
temp = lib.einsum('jaki,i->ajk', eris_ovoo, r_a, optimize=True)
temp -= lib.einsum('kaji,i->ajk', eris_ovoo, r_a, optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
s[s_bab:f_bab] += lib.einsum('jaik,i->ajk', eris_OVoo, r_a, optimize=True).reshape(-1)
s[s_aba:f_aba] += lib.einsum('jaki,i->ajk', eris_ovOO, r_b, optimize=True).reshape(-1)
temp = lib.einsum('jaki,i->ajk', eris_OVOO, r_b, optimize=True)
temp -= lib.einsum('kaji,i->ajk', eris_OVOO, r_b, optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
############ ADC(2) ajk - bil block ############################
r_aaa = r_aaa.reshape(-1)
r_bbb = r_bbb.reshape(-1)
s[s_aaa:f_aaa] += D_aij_a * r_aaa
s[s_bab:f_bab] += D_aij_bab * r_bab.reshape(-1)
s[s_aba:f_aba] += D_aij_aba * r_aba.reshape(-1)
s[s_bbb:f_bbb] += D_aij_b * r_bbb
############### ADC(3) ajk - bil block ############################
if (method == "adc(2)-x" or method == "adc(3)"):
eris_oooo = eris.oooo
eris_OOOO = eris.OOOO
eris_ooOO = eris.ooOO
eris_oovv = eris.oovv
eris_OOVV = eris.OOVV
eris_ooVV = eris.ooVV
eris_OOvv = eris.OOvv
eris_ovvo = eris.ovvo
eris_OVVO = eris.OVVO
eris_ovVO = eris.ovVO
eris_OVvo = eris.OVvo
r_aaa = r_aaa.reshape(nvir_a,-1)
r_bab = r_bab.reshape(nvir_b,nocc_b,nocc_a)
r_aba = r_aba.reshape(nvir_a,nocc_a,nocc_b)
r_bbb = r_bbb.reshape(nvir_b,-1)
r_aaa_u = None
r_aaa_u = np.zeros((nvir_a,nocc_a,nocc_a))
r_aaa_u[:,ij_ind_a[0],ij_ind_a[1]]= r_aaa.copy()
r_aaa_u[:,ij_ind_a[1],ij_ind_a[0]]= -r_aaa.copy()
r_bbb_u = None
r_bbb_u = np.zeros((nvir_b,nocc_b,nocc_b))
r_bbb_u[:,ij_ind_b[0],ij_ind_b[1]]= r_bbb.copy()
r_bbb_u[:,ij_ind_b[1],ij_ind_b[0]]= -r_bbb.copy()
temp = 0.5*lib.einsum('jlki,ail->ajk',eris_oooo,r_aaa_u ,optimize=True)
temp -= 0.5*lib.einsum('jikl,ail->ajk',eris_oooo,r_aaa_u ,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
temp = 0.5*lib.einsum('jlki,ail->ajk',eris_OOOO,r_bbb_u,optimize=True)
temp -= 0.5*lib.einsum('jikl,ail->ajk',eris_OOOO,r_bbb_u,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
s[s_bab:f_bab] -= 0.5*lib.einsum('kijl,ali->ajk',eris_ooOO,
r_bab,optimize=True).reshape(-1)
s[s_bab:f_bab] -= 0.5*lib.einsum('klji,ail->ajk',eris_ooOO,
r_bab,optimize=True).reshape(-1)
s[s_aba:f_aba] -= 0.5*lib.einsum('jlki,ali->ajk',eris_ooOO,
r_aba,optimize=True).reshape(-1)
s[s_aba:f_aba] -= 0.5*lib.einsum('jikl,ail->ajk',eris_ooOO,
r_aba,optimize=True).reshape(-1)
temp = 0.5*lib.einsum('klba,bjl->ajk',eris_oovv,r_aaa_u,optimize=True)
temp -= 0.5*lib.einsum('kabl,bjl->ajk',eris_ovvo,r_aaa_u,optimize=True)
temp += 0.5* lib.einsum('kabl,blj->ajk',eris_ovVO,r_bab,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
s[s_bab:f_bab] += 0.5*lib.einsum('klba,bjl->ajk',eris_ooVV,
r_bab,optimize=True).reshape(-1)
temp_1 = 0.5*lib.einsum('klba,bjl->ajk',eris_OOVV,r_bbb_u,optimize=True)
temp_1 -= 0.5*lib.einsum('kabl,bjl->ajk',eris_OVVO,r_bbb_u,optimize=True)
temp_1 += 0.5*lib.einsum('kabl,blj->ajk',eris_OVvo,r_aba,optimize=True)
s[s_bbb:f_bbb] += temp_1[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
s[s_aba:f_aba] += 0.5*lib.einsum('klba,bjl->ajk',eris_OOvv,
r_aba,optimize=True).reshape(-1)
temp = -0.5*lib.einsum('jlba,bkl->ajk',eris_oovv,r_aaa_u,optimize=True)
temp += 0.5*lib.einsum('jabl,bkl->ajk',eris_ovvo,r_aaa_u,optimize=True)
temp -= 0.5*lib.einsum('jabl,blk->ajk',eris_ovVO,r_bab,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
s[s_bab:f_bab] += 0.5*lib.einsum('jabl,bkl->ajk',
eris_OVvo,r_aaa_u,optimize=True).reshape(-1)
s[s_bab:f_bab] += 0.5*lib.einsum('jlba,blk->ajk',
eris_OOVV,r_bab,optimize=True).reshape(-1)
s[s_bab:f_bab] -= 0.5*lib.einsum('jabl,blk->ajk',
eris_OVVO,r_bab,optimize=True).reshape(-1)
temp = -0.5*lib.einsum('jlba,bkl->ajk',eris_OOVV,r_bbb_u,optimize=True)
temp += 0.5*lib.einsum('jabl,bkl->ajk',eris_OVVO,r_bbb_u,optimize=True)
temp -= 0.5*lib.einsum('jabl,blk->ajk',eris_OVvo,r_aba,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
s[s_aba:f_aba] += 0.5*lib.einsum('jlba,blk->ajk',eris_oovv,
r_aba,optimize=True).reshape(-1)
s[s_aba:f_aba] -= 0.5*lib.einsum('jabl,blk->ajk',eris_ovvo,
r_aba,optimize=True).reshape(-1)
s[s_aba:f_aba] += 0.5*lib.einsum('jabl,bkl->ajk',eris_ovVO,
r_bbb_u,optimize=True).reshape(-1)
temp = -0.5*lib.einsum('kiba,bij->ajk',eris_oovv,r_aaa_u,optimize=True)
temp += 0.5*lib.einsum('kabi,bij->ajk',eris_ovvo,r_aaa_u,optimize=True)
temp += 0.5*lib.einsum('kabi,bij->ajk',eris_ovVO,r_bab,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
s[s_bab:f_bab] += 0.5*lib.einsum('kiba,bji->ajk',eris_ooVV,
r_bab,optimize=True).reshape(-1)
temp = -0.5*lib.einsum('kiba,bij->ajk',eris_OOVV,r_bbb_u,optimize=True)
temp += 0.5*lib.einsum('kabi,bij->ajk',eris_OVVO,r_bbb_u,optimize=True)
temp += 0.5*lib.einsum('kabi,bij->ajk',eris_OVvo,r_aba,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
s[s_aba:f_aba] += 0.5*lib.einsum('kiba,bji->ajk',eris_OOvv,
r_aba,optimize=True).reshape(-1)
temp = 0.5*lib.einsum('jiba,bik->ajk',eris_oovv,r_aaa_u,optimize=True)
temp -= 0.5*lib.einsum('jabi,bik->ajk',eris_ovvo,r_aaa_u,optimize=True)
temp -= 0.5*lib.einsum('jabi,bik->ajk',eris_ovVO,r_bab,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1]].reshape(-1)
s[s_bab:f_bab] += 0.5*lib.einsum('jiba,bik->ajk',eris_OOVV,
r_bab,optimize=True).reshape(-1)
s[s_bab:f_bab] -= 0.5*lib.einsum('jabi,bik->ajk',eris_OVVO,
r_bab,optimize=True).reshape(-1)
s[s_bab:f_bab] -= 0.5*lib.einsum('jabi,bik->ajk',eris_OVvo,
r_aaa_u,optimize=True).reshape(-1)
s[s_aba:f_aba] += 0.5*lib.einsum('jiba,bik->ajk',eris_oovv,
r_aba,optimize=True).reshape(-1)
s[s_aba:f_aba] -= 0.5*lib.einsum('jabi,bik->ajk',eris_ovvo,
r_aba,optimize=True).reshape(-1)
s[s_aba:f_aba] -= 0.5*lib.einsum('jabi,bik->ajk',eris_ovVO,
r_bbb_u,optimize=True).reshape(-1)
temp = 0.5*lib.einsum('jiba,bik->ajk',eris_OOVV,r_bbb_u,optimize=True)
temp -= 0.5*lib.einsum('jabi,bik->ajk',eris_OVVO,r_bbb_u,optimize=True)
temp -= 0.5*lib.einsum('jabi,bik->ajk',eris_OVvo,r_aba,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1]].reshape(-1)
if (method == "adc(3)"):
eris_ovoo = eris.ovoo
eris_OVOO = eris.OVOO
eris_ovOO = eris.ovOO
eris_OVoo = eris.OVoo
################ ADC(3) i - kja and ajk - i block ############################
t2_1_a = adc.t2[0][0][:]
t2_1_ab = adc.t2[0][1][:]
temp_singles = np.zeros(nocc_a)
temp_doubles = np.zeros((nvir_a, nvir_a, nvir_a))
r_aaa = r_aaa.reshape(nvir_a,-1)
t2_1_a_t = t2_1_a[ij_ind_a[0],ij_ind_a[1],:,:]
temp_1 = lib.einsum('pbc,ap->abc',t2_1_a_t,r_aaa, optimize=True)
if eris.ovvv is None:
chnk_size = uadc_ao2mo.calculate_chunk_size(adc)
for a,b in lib.prange(0,nocc_a,chnk_size):
eris_ovvv = dfadc.get_ovvv_spin_df(
adc, eris.Lov, eris.Lvv, a, chnk_size).reshape(-1,nvir_a,nvir_a,nvir_a)
temp_singles[a:b] += 0.5* \
lib.einsum('abc,icab->i',temp_1, eris_ovvv, optimize=True)
temp_singles[a:b] -= 0.5* \
lib.einsum('abc,ibac->i',temp_1, eris_ovvv, optimize=True)
temp_doubles += lib.einsum('i,icab->bca',r_a[a:b],eris_ovvv,optimize=True)
temp_doubles -= lib.einsum('i,ibac->bca',r_a[a:b],eris_ovvv,optimize=True)
del eris_ovvv
else :
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir_a)
temp_singles += 0.5*lib.einsum('abc,icab->i',temp_1, eris_ovvv, optimize=True)
temp_singles -= 0.5*lib.einsum('abc,ibac->i',temp_1, eris_ovvv, optimize=True)
temp_doubles += lib.einsum('i,icab->bca',r_a,eris_ovvv,optimize=True)
temp_doubles -= lib.einsum('i,ibac->bca',r_a,eris_ovvv,optimize=True)
del eris_ovvv
s[s_a:f_a] += temp_singles
s[s_aaa:f_aaa] += 0.5*lib.einsum('bca,pbc->ap',temp_doubles,
t2_1_a_t,optimize=True).reshape(-1)
del temp_singles
del temp_doubles
r_aaa_u = np.zeros((nvir_a,nocc_a,nocc_a))
r_aaa_u[:,ij_ind_a[0],ij_ind_a[1]]= r_aaa.copy()
r_aaa_u[:,ij_ind_a[1],ij_ind_a[0]]= -r_aaa.copy()
r_aba = r_aba.reshape(nvir_a,nocc_a,nocc_b)
temp = lib.einsum('jlab,ajk->blk',t2_1_a,r_aaa_u,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blk,lbik->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blk,iblk->i',temp,eris_ovoo,optimize=True)
temp_1 = lib.einsum('jlab,ajk->blk',t2_1_a,r_aba,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blk,lbik->i',temp_1,eris_ovOO,optimize=True)
temp = -lib.einsum('klab,akj->blj',t2_1_a,r_aaa_u,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blj,lbij->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blj,iblj->i',temp,eris_ovoo,optimize=True)
temp_1 = -lib.einsum('klab,akj->blj',t2_1_a,r_aba,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blj,lbij->i',temp_1,eris_ovOO,optimize=True)
temp_1 = lib.einsum('i,lbik->kbl',r_a, eris_ovoo)
temp_1 -= lib.einsum('i,iblk->kbl',r_a, eris_ovoo)
temp = lib.einsum('kbl,jlab->ajk',temp_1,t2_1_a,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1] ].reshape(-1)
temp_2 = lib.einsum('i,lbik->kbl',r_b,eris_ovOO)
temp = lib.einsum('kbl,jlab->ajk',temp_2,t2_1_a,optimize=True)
s[s_aba:f_aba] += temp.reshape(-1)
temp_1 = lib.einsum('i,lbij->jbl',r_a, eris_ovoo)
temp_1 -= lib.einsum('i,iblj->jbl',r_a, eris_ovoo)
temp = lib.einsum('jbl,klab->ajk',temp_1,t2_1_a,optimize=True)
s[s_aaa:f_aaa] -= temp[:,ij_ind_a[0],ij_ind_a[1] ].reshape(-1)
del t2_1_a
t2_1_b = adc.t2[0][2][:]
temp_singles = np.zeros(nocc_b)
temp_doubles = np.zeros((nvir_b, nvir_b, nvir_b))
r_bbb = r_bbb.reshape(nvir_b,-1)
t2_1_b_t = t2_1_b[ij_ind_b[0],ij_ind_b[1],:,:]
temp_1 = lib.einsum('pbc,ap->abc',t2_1_b_t,r_bbb, optimize=True)
if eris.OVVV is None:
chnk_size = uadc_ao2mo.calculate_chunk_size(adc)
a = 0
for a,b in lib.prange(0,nocc_b,chnk_size):
eris_OVVV = dfadc.get_ovvv_spin_df(
adc, eris.LOV, eris.LVV, a, chnk_size).reshape(-1,nvir_b,nvir_b,nvir_b)
temp_singles[a:b] += 0.5* \
lib.einsum('abc,icab->i',temp_1, eris_OVVV, optimize=True)
temp_singles[a:b] -= 0.5* \
lib.einsum('abc,ibac->i',temp_1, eris_OVVV, optimize=True)
temp_doubles += lib.einsum('i,icab->bca',r_b[a:b],eris_OVVV,optimize=True)
temp_doubles -= lib.einsum('i,ibac->bca',r_b[a:b],eris_OVVV,optimize=True)
del eris_OVVV
else :
eris_OVVV = radc_ao2mo.unpack_eri_1(eris.OVVV, nvir_b)
temp_singles += 0.5*lib.einsum('abc,icab->i',temp_1, eris_OVVV, optimize=True)
temp_singles -= 0.5*lib.einsum('abc,ibac->i',temp_1, eris_OVVV, optimize=True)
temp_doubles += lib.einsum('i,icab->bca',r_b,eris_OVVV,optimize=True)
temp_doubles -= lib.einsum('i,ibac->bca',r_b,eris_OVVV,optimize=True)
del eris_OVVV
s[s_b:f_b] += temp_singles
s[s_bbb:f_bbb] += 0.5*lib.einsum('bca,pbc->ap',temp_doubles,
t2_1_b_t,optimize=True).reshape(-1)
del temp_singles
del temp_doubles
r_bbb_u = np.zeros((nvir_b,nocc_b,nocc_b))
r_bbb_u[:,ij_ind_b[0],ij_ind_b[1]]= r_bbb.copy()
r_bbb_u[:,ij_ind_b[1],ij_ind_b[0]]= -r_bbb.copy()
r_bab = r_bab.reshape(nvir_b,nocc_b,nocc_a)
temp_1 = lib.einsum('jlab,ajk->blk',t2_1_b,r_bab,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blk,lbik->i',temp_1,eris_OVoo,optimize=True)
temp = lib.einsum('jlab,ajk->blk',t2_1_b,r_bbb_u,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blk,lbik->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blk,iblk->i',temp,eris_OVOO,optimize=True)
temp_1 = -lib.einsum('klab,akj->blj',t2_1_b,r_bab,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blj,lbij->i',temp_1,eris_OVoo,optimize=True)
temp = -lib.einsum('klab,akj->blj',t2_1_b,r_bbb_u,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blj,lbij->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blj,iblj->i',temp,eris_OVOO,optimize=True)
temp_2 = lib.einsum('i,lbik->kbl',r_a,eris_OVoo)
temp = lib.einsum('kbl,jlab->ajk',temp_2,t2_1_b,optimize=True)
s[s_bab:f_bab] += temp.reshape(-1)
temp_1 = lib.einsum('i,lbik->kbl',r_b, eris_OVOO)
temp_1 -= lib.einsum('i,iblk->kbl',r_b, eris_OVOO)
temp = lib.einsum('kbl,jlab->ajk',temp_1,t2_1_b,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1] ].reshape(-1)
temp_1 = lib.einsum('i,lbij->jbl',r_b, eris_OVOO)
temp_1 -= lib.einsum('i,iblj->jbl',r_b, eris_OVOO)
temp = lib.einsum('jbl,klab->ajk',temp_1,t2_1_b,optimize=True)
s[s_bbb:f_bbb] -= temp[:,ij_ind_b[0],ij_ind_b[1] ].reshape(-1)
del t2_1_b
temp_1 = lib.einsum('kjcb,ajk->abc',t2_1_ab,r_bab, optimize=True)
temp_2 = np.zeros((nvir_a, nvir_b, nvir_b))
if eris.ovVV is None:
chnk_size = uadc_ao2mo.calculate_chunk_size(adc)
for a,b in lib.prange(0,nocc_a,chnk_size):
eris_ovVV = dfadc.get_ovvv_spin_df(
adc, eris.Lov, eris.LVV, a, chnk_size).reshape(-1,nvir_a,nvir_b,nvir_b)
s[s_a:f_a][a:b] += lib.einsum('abc,icab->i',temp_1, eris_ovVV, optimize=True)
temp_2 += lib.einsum('i,icab->cba',r_a[a:b],eris_ovVV,optimize=True)
del eris_ovVV
else :
eris_ovVV = radc_ao2mo.unpack_eri_1(eris.ovVV, nvir_b)
s[s_a:f_a] += lib.einsum('abc,icab->i',temp_1, eris_ovVV, optimize=True)
temp_2 += lib.einsum('i,icab->cba',r_a,eris_ovVV,optimize=True)
del eris_ovVV
s[s_bab:f_bab] += lib.einsum('cba,kjcb->ajk',temp_2, t2_1_ab, optimize=True).reshape(-1)
del temp_1
del temp_2
temp_1 = lib.einsum('jkbc,ajk->abc',t2_1_ab,r_aba, optimize=True)
temp_2 = np.zeros((nvir_a, nvir_b, nvir_a))
if eris.OVvv is None:
chnk_size = uadc_ao2mo.calculate_chunk_size(adc)
a = 0
for a,b in lib.prange(0,nocc_b,chnk_size):
eris_OVvv = dfadc.get_ovvv_spin_df(
adc, eris.LOV, eris.Lvv, a, chnk_size).reshape(-1,nvir_b,nvir_a,nvir_a)
s[s_b:f_b][a:b] += lib.einsum('abc,icab->i',temp_1, eris_OVvv, optimize=True)
temp_2 += lib.einsum('i,icab->bca',r_b[a:b],eris_OVvv,optimize=True)
del eris_OVvv
else :
eris_OVvv = radc_ao2mo.unpack_eri_1(eris.OVvv, nvir_a)
s[s_b:f_b] += lib.einsum('abc,icab->i',temp_1, eris_OVvv, optimize=True)
temp_2 += lib.einsum('i,icab->bca',r_b,eris_OVvv,optimize=True)
del eris_OVvv
s[s_aba:f_aba] += lib.einsum('bca,jkbc->ajk',temp_2, t2_1_ab, optimize=True).reshape(-1)
del temp_1
del temp_2
temp = lib.einsum('ljba,ajk->blk',t2_1_ab,r_bab,optimize=True)
temp_1 = lib.einsum('jlab,ajk->blk',t2_1_ab,r_aaa_u,optimize=True)
temp_2 = lib.einsum('jlba,akj->blk',t2_1_ab,r_bab, optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blk,lbik->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blk,iblk->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blk,lbik->i',temp_1,eris_OVoo,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blk,iblk->i',temp_2,eris_ovOO,optimize=True)
temp = lib.einsum('jlab,ajk->blk',t2_1_ab,r_aba,optimize=True)
temp_1 = lib.einsum('ljba,ajk->blk',t2_1_ab,r_bbb_u,optimize=True)
temp_2 = lib.einsum('ljab,akj->blk',t2_1_ab,r_aba,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blk,lbik->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blk,iblk->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blk,lbik->i',temp_1,eris_ovOO,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blk,iblk->i',temp_2,eris_OVoo,optimize=True)
temp = -lib.einsum('lkba,akj->blj',t2_1_ab,r_bab,optimize=True)
temp_1 = -lib.einsum('klab,akj->blj',t2_1_ab,r_aaa_u,optimize=True)
temp_2 = -lib.einsum('klba,ajk->blj',t2_1_ab,r_bab,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blj,lbij->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blj,iblj->i',temp,eris_ovoo,optimize=True)
s[s_a:f_a] -= 0.5*lib.einsum('blj,lbij->i',temp_1,eris_OVoo,optimize=True)
s[s_a:f_a] += 0.5*lib.einsum('blj,iblj->i',temp_2,eris_ovOO,optimize=True)
temp = -lib.einsum('klab,akj->blj',t2_1_ab,r_aba,optimize=True)
temp_1 = -lib.einsum('lkba,akj->blj',t2_1_ab,r_bbb_u,optimize=True)
temp_2 = -lib.einsum('lkab,ajk->blj',t2_1_ab,r_aba,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blj,lbij->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blj,iblj->i',temp,eris_OVOO,optimize=True)
s[s_b:f_b] -= 0.5*lib.einsum('blj,lbij->i',temp_1,eris_ovOO,optimize=True)
s[s_b:f_b] += 0.5*lib.einsum('blj,iblj->i',temp_2,eris_OVoo,optimize=True)
temp_2 = lib.einsum('i,lbik->kbl',r_a, eris_OVoo)
temp = lib.einsum('kbl,jlab->ajk',temp_2,t2_1_ab,optimize=True)
s[s_aaa:f_aaa] += temp[:,ij_ind_a[0],ij_ind_a[1] ].reshape(-1)
temp_1 = lib.einsum('i,lbik->kbl',r_a,eris_ovoo)
temp_1 -= lib.einsum('i,iblk->kbl',r_a,eris_ovoo)
temp = lib.einsum('kbl,ljba->ajk',temp_1,t2_1_ab,optimize=True)
s[s_bab:f_bab] += temp.reshape(-1)
temp_2 = lib.einsum('i,lbik->kbl',r_b, eris_ovOO)
temp = lib.einsum('kbl,ljba->ajk',temp_2,t2_1_ab,optimize=True)
s[s_bbb:f_bbb] += temp[:,ij_ind_b[0],ij_ind_b[1] ].reshape(-1)
temp_1 = lib.einsum('i,lbik->kbl',r_b,eris_OVOO)
temp_1 -= lib.einsum('i,iblk->kbl',r_b,eris_OVOO)
temp = lib.einsum('kbl,jlab->ajk',temp_1,t2_1_ab,optimize=True)
s[s_aba:f_aba] += temp.reshape(-1)
temp_2 = lib.einsum('i,lbij->jbl',r_a, eris_OVoo)
temp = lib.einsum('jbl,klab->ajk',temp_2,t2_1_ab,optimize=True)
s[s_aaa:f_aaa] -= temp[:,ij_ind_a[0],ij_ind_a[1] ].reshape(-1)
temp = -lib.einsum('i,iblj->jbl',r_a,eris_ovOO,optimize=True)
temp_1 = -lib.einsum('jbl,klba->ajk',temp,t2_1_ab,optimize=True)
s[s_bab:f_bab] -= temp_1.reshape(-1)
temp_2 = lib.einsum('i,lbij->jbl',r_b, eris_ovOO)
temp = lib.einsum('jbl,lkba->ajk',temp_2,t2_1_ab,optimize=True)
s[s_bbb:f_bbb] -= temp[:,ij_ind_b[0],ij_ind_b[1] ].reshape(-1)
temp = -lib.einsum('i,iblj->jbl',r_b,eris_OVoo,optimize=True)
temp_1 = -lib.einsum('jbl,lkab->ajk',temp,t2_1_ab,optimize=True)
s[s_aba:f_aba] -= temp_1.reshape(-1)
del t2_1_ab
cput0 = log.timer_debug1("completed sigma vector calculation", *cput0)
s *= -1.0